Fill in the blank with the correct inequality symbol. State which property of inequalities is being utilized.
If [tex]\frac{1}{5} x \leq 2[/tex], then [tex]x[/tex] [ ] 10.
Which of the following properties is being utilized?
A. Multiplication Property
B. Addition Property
Answer (1)
Multiply both sides of the inequality 5 1 x ≤ 2 by 5.
This isolates x and gives x ≤ 10 .
The property used is the multiplication property of inequality.
Therefore, the answer is x ≤ 10 .
Explanation
Analyzing the Inequality We are given the inequality 5 1 x ≤ 2 . Our goal is to isolate x on one side of the inequality to determine its relationship with a constant value. To do this, we will use the multiplication property of inequalities.
Isolating x To isolate x , we need to eliminate the fraction 5 1 that is multiplying x . We can do this by multiplying both sides of the inequality by 5. Since 5 is a positive number, multiplying both sides by 5 will not change the direction of the inequality.
Applying Multiplication Multiplying both sides of the inequality 5 1 x ≤ 2 by 5, we get: 5 × 5 1 x ≤ 5 × 2 x ≤ 10
Final Answer Therefore, if 5 1 x ≤ 2 , then x ≤ 10 . The property of inequalities used here is the multiplication property.
Examples
Imagine you're baking a cake and the recipe calls for 5 1 cup of sugar per serving. If you want to make at most 2 servings, the inequality 5 1 x ≤ 2 helps you determine the maximum amount of sugar, x , you'll need. By solving the inequality, you find that you need at most 10 cups of sugar. This concept is useful in scaling recipes, managing budgets, or any situation where you need to adjust quantities while staying within certain limits.
